The only totally unidentifiable piece of apparatus in the place was one queer contriance at one side. It looked partly like a machine gun because of a long brass barrel projecting from it...

Von Holtz moved to that contrivance, removed a cap from the end of the brass tube, looked carefully into the opening, and waved stiffly for Tommy to look in...

There was a lens in the end of the brass tube. It was, in fact, nothing less than a telescope apparently looking at something in a closed box... He looked into the telescope, and he was seeing outdoors... Through the thick walls of the laboratory. He was gazing upon a landscape such as should not - such as could not - exist upon the earth.

Impossible technologies required explanation in the 'Thirties; people did not suspend their disbelief as easily as we do today when presented with computer graphics that look real. How can you look into the fifth dimension?

Here's the explanation presented by the author:

The objective-glass at the end of the telescope faced a mirror, which was inclined to its face at an angle of forty-five degrees. A beam of light from the objective would be reflected to a second mirror, twisted in a fashion curiously askew. Then the light would go to a third mirror...

Tommy looked at that third mirror, and instantly his eyes ached... He could see the third mirror, but his eyes hurt the instant they looked upon it, as if that third mirror were distorted in an impossible fashion... He could see, though, that somehow that third mirror would reflect his imaginary beam of light into a fourth mirror of which he could see only the edge...

"A mirror of forty-five degrees," said Von Holtz precisely, "reflects light at a right angle. There are four mirrors, and each bends a ray of light through a right angle which is also a right angle to all the others. The result is that the dimensoscope looks into what is a fifth dimension, into which no man ever looked before."